when you pay for the download, instead of it downloading directly, you get an Amazon Download file and you use the Amazon MP3 downloader software it prompts you to install to download the actual MP3 files.

Amazon's download service is pretty terrible. A few times I've accidentally bought a track with the fucking One Click button, scrambled around trying to cancel it, found out I can't and then went to download the track anyway, only to find out I couldn't get back to it after exiting the download screen. There doesn't seem to be a page for all your past downloads like on Play.com etc.